It depends on context, really. If you are talking about a "grand éléphant", it means it is tall (vs baby or vs small) and the same applies to bears.
"un gros éléphant" or "un gros ours" refer to their respective volume.

Just as for "le chat" and "le chien", the generic animal is masculine by default.

The same applies to animals having a feminine noun: une fourmi, une girafe, une souris... all of these are used when you don't know whether the animal is male of female. If you know that the ant, giraffe or mouse is male, you use "une fourmi mâle, une girafe mâle, une souris mâle".